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Server: Apache/2.4.46 (Win64) OpenSSL/1.1.1j PHP/8.4.25
System: Windows NT DESKTOP-4TAV2RJ 10.0 build 19045 (Windows 10) AMD64
User: fred (0)
PHP: 8.4.25
Disabled: NONE
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File: C:/Users/fred/anaconda3/Lib/site-packages/scipy/sparse/csgraph/_shortest_path.cp312-win_amd64.pyd
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Routines for performing shortest-path graph searches

The main interface is in the function :func:`shortest_path`.  This
calls cython routines that compute the shortest path using
the Floyd-Warshall algorithm, Dijkstra's algorithm with Fibonacci Heaps,
the Bellman-Ford algorithm, or Johnson's Algorithm.
: ASCIIAll dimensions preceding dimension %d must be indexed and not slicedAssertionErrorBFBuffer view does not expose stridesCC:\b\abs_efv75hqhju\croot\scipy_1717521501389\work\scipy\sparse\csgraph\_shortest_path.pyxCan only create a buffer that is contiguous in memory.Cannot assign to read-only memoryviewCannot create writable memory view from read-only memoryviewCannot index with type 'Cannot specify indices with method == 'FW'.Cannot transpose memoryview with indirect dimensionsDDTYPEDimension %d is not directEllipsisEmpty shape tuple for cython.arrayFWFailed to allocate memory in _dijkstra_directedFailed to allocate memory in _dijkstra_directed_multiFailed to allocate memory in _dijkstra_undirectedFailed to allocate memory in _dijkstra_undirected_multiGraph has negative weights: dijkstra will give inaccurate results if the graph contains negative cycles. Consider johnson or bellman_ford.ITYPEImportErrorIncompatible checksums (0x%x vs (0x82a3537, 0x6ae9995, 0xb068931) = (name))IndexErrorIndex out of bounds (axis %d)Indirect dimensions not supportedInvalid mode, expected 'c' or 'fortran', got Invalid shape in axis JMemoryError<MemoryView of %r at 0x%x><MemoryView of %r object>NNegativeCycleErrorNegativeCycleError.__init__Negative cycle detected on node %iNegative cycle in nodes %sNkOOut of bounds on buffer access (axis PickleErrorSequenceStep may not be zero (axis %d)TTypeErrorUnable to convert item to objectValueErrorView.MemoryView.*?')abcallocate_buffer and anyarangearrayasyncio.coroutinesatleast_1dautobasebellman_ford
    bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False,
                 unweighted=False)

    Compute the shortest path lengths using the Bellman-Ford algorithm.

    The Bellman-Ford algorithm can robustly deal with graphs with negative
    weights.  If a negative cycle is detected, an error is raised.  For
    graphs without negative edge weights, Dijkstra's algorithm may be faster.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    This routine is specially designed for graphs with negative edge weights.
    If all edge weights are positive, then Dijkstra's algorithm is a better
    choice.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import bellman_ford

    >>> graph = [
    ... [0, 1 ,2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

    >>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    bellman_ford (line 927)c__class____class_getitem__cline_in_tracebackcollectionscollections.abccompressed<contiguous and direct><contiguous and indirect>convert_pydata_sparse_to_scipycoocopycopy_if_densecopy_if_sparsecountcsccsgraphcsgraphTcsrcsrT_datacsr_datacsr_matrixcsr_outputdatadense_outputdiagonal__dict__dijkstra
    dijkstra(csgraph, directed=True, indices=None, return_predecessors=False,
             unweighted=False, limit=np.inf, min_only=False)

    Dijkstra algorithm using Fibonacci Heaps

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of non-negative distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j] and from
        point j to i along paths csgraph[j, i].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j or j to i along either
        csgraph[i, j] or csgraph[j, i].
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.
    limit : float, optional
        The maximum distance to calculate, must be >= 0. Using a smaller limit
        will decrease computation time by aborting calculations between pairs
        that are separated by a distance > limit. For such pairs, the distance
        will be equal to np.inf (i.e., not connected).

        .. versionadded:: 0.14.0
    min_only : bool, optional
        If False (default), for every node in the graph, find the shortest path
        from every node in indices.
        If True, for every node in the graph, find the shortest path from any
        of the nodes in indices (which can be substantially faster).

        .. versionadded:: 1.3.0

    Returns
    -------
    dist_matrix : ndarray, shape ([n_indices, ]n_nodes,)
        The matrix of distances between graph nodes. If min_only=False,
        dist_matrix has shape (n_indices, n_nodes) and dist_matrix[i, j]
        gives the shortest distance from point i to point j along the graph.
        If min_only=True, dist_matrix has shape (n_nodes,) and contains for
        a given node the shortest path to that node from any of the nodes
        in indices.
    predecessors : ndarray, shape ([n_indices, ]n_nodes,)
        If min_only=False, this has shape (n_indices, n_nodes),
        otherwise it has shape (n_nodes,).
        Returned only if return_predecessors == True.
        The matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    sources : ndarray, shape (n_nodes,)
        Returned only if min_only=True and return_predecessors=True.
        Contains the index of the source which had the shortest path
        to each target.  If no path exists within the limit,
        this will contain -9999.  The value at the indices passed
        will be equal to that index (i.e. the fastest way to reach
        node i, is to start on node i).

    Notes
    -----
    As currently implemented, Dijkstra's algorithm does not work for
    graphs with direction-dependent distances when directed == False.
    i.e., if csgraph[i,j] and csgraph[j,i] are not equal and
    both are nonzero, setting directed=False will not yield the correct
    result.

    Also, this routine does not work for graphs with negative
    distances.  Negative distances can lead to infinite cycles that must
    be handled by specialized algorithms such as Bellman-Ford's algorithm
    or Johnson's algorithm.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import dijkstra

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [0, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 3)	3

    >>> dist_matrix, predecessors = dijkstra(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    dijkstra (line 415)directeddisabledist_arraydist_matrix__doc__dtypedtype_is_objectedgesemptyenableencodeenumerateerrorfillflagsflatfloat64floyd_warshall
    floyd_warshall(csgraph, directed=True, return_predecessors=False,
                   unweighted=False, overwrite=False)

    Compute the shortest path lengths using the Floyd-Warshall algorithm

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.
    overwrite : bool, optional
        If True, overwrite csgraph with the result.  This applies only if
        csgraph is a dense, c-ordered array with dtype=float64.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import floyd_warshall

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3


    >>> dist_matrix, predecessors = floyd_warshall(csgraph=graph, directed=False, return_predecessors=True)
    >>> dist_matrix
    array([[0., 1., 2., 2.],
           [1., 0., 3., 1.],
           [2., 3., 0., 3.],
           [2., 1., 3., 0.]])
    >>> predecessors
    array([[-9999,     0,     0,     1],
           [    1, -9999,     0,     1],
           [    2,     0, -9999,     2],
           [    1,     3,     3, -9999]], dtype=int32)

    floyd_warshall (line 224)formatfortranfullgc__getstate__ (got got differing extents in dimension id__import__indexindicesindices out of range 0...Nindptrinf__init____init_subclass___initializingint32isMaskedArray_is_coroutineis_sparseisenabledisfiniteisinfissparseitemsizeitemsize <= 0 for cython.arrayjohnson
    johnson(csgraph, directed=True, indices=None, return_predecessors=False,
            unweighted=False)

    Compute the shortest path lengths using Johnson's algorithm.

    Johnson's algorithm combines the Bellman-Ford algorithm and Dijkstra's
    algorithm to quickly find shortest paths in a way that is robust to
    the presence of negative cycles.  If a negative cycle is detected,
    an error is raised.  For graphs without negative edge weights,
    dijkstra may be faster.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    This routine is specially designed for graphs with negative edge weights.
    If all edge weights are positive, then Dijkstra's algorithm is a better
    choice.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import johnson

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

    >>> dist_matrix, predecessors = johnson(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    johnson (line 1162)limitlimit must be >= 0limitfma__main__memviewmessage__metaclass__methodmin_onlymode__module____mro_entries__name__name__ndim__new__nnzno default __reduce__ due to non-trivial __cinit__npnumpynumpy.core.multiarray failed to importnumpy.core.umath failed to importobjonesorderoverwritepackpicklepredecessor_matrix__prepare____pyx_PickleError__pyx_checksum__pyx_result__pyx_state__pyx_type__pyx_unpickle_Enum__pyx_vtable____qualname__range__reduce____reduce_cython____reduce_ex__registerreshaperetreturn_predecessorsreturn_shapescipy.sparsescipy.sparse._sputilsscipy.sparse.csgraph._shortest_pathscipy.sparse.csgraph._validationself__set_name____setstate____setstate_cython__shapeshortest_path
    shortest_path(csgraph, method='auto', directed=True, return_predecessors=False,
                  unweighted=False, overwrite=False, indices=None)

    Perform a shortest-path graph search on a positive directed or
    undirected graph.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    method : string ['auto'|'FW'|'D'], optional
        Algorithm to use for shortest paths.  Options are:

           'auto' -- (default) select the best among 'FW', 'D', 'BF', or 'J'
                     based on the input data.

           'FW'   -- Floyd-Warshall algorithm.
                     Computational cost is approximately ``O[N^3]``.
                     The input csgraph will be converted to a dense representation.

           'D'    -- Dijkstra's algorithm with Fibonacci heaps.
                     Computational cost is approximately ``O[N(N*k + N*log(N))]``,
                     where ``k`` is the average number of connected edges per node.
                     The input csgraph will be converted to a csr representation.

           'BF'   -- Bellman-Ford algorithm.
                     This algorithm can be used when weights are negative.
                     If a negative cycle is encountered, an error will be raised.
                     Computational cost is approximately ``O[N(N^2 k)]``, where 
                     ``k`` is the average number of connected edges per node. 
                     The input csgraph will be converted to a csr representation.

           'J'    -- Johnson's algorithm.
                     Like the Bellman-Ford algorithm, Johnson's algorithm is 
                     designed for use when the weights are negative. It combines 
                     the Bellman-Ford algorithm with Dijkstra's algorithm for 
                     faster computation.

    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.
    overwrite : bool, optional
        If True, overwrite csgraph with the result.  This applies only if
        method == 'FW' and csgraph is a dense, c-ordered array with
        dtype=float64.
    indices : array_like or int, optional
        If specified, only compute the paths from the points at the given
        indices. Incompatible with method == 'FW'.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.
    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    As currently implemented, Dijkstra's algorithm and Johnson's algorithm
    do not work for graphs with direction-dependent distances when
    directed == False.  i.e., if csgraph[i,j] and csgraph[j,i] are non-equal
    edges, method='D' may yield an incorrect result.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import shortest_path

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

    >>> dist_matrix, predecessors = shortest_path(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    shortest_path (line 39)sizesource_matrix__spec__startstepstop<strided and direct><strided and direct or indirect><strided and indirect><stringsource>structsupersys__test__tocootocsrunable to allocate array data.unable to allocate shape and strides.unpackunrecognized method '%s'unweightedupdatevalidate_graphversion_infowarnwarningswherezeros00010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899
    shortest_path(csgraph, method='auto', directed=True, return_predecessors=False,
                  unweighted=False, overwrite=False, indices=None)

    Perform a shortest-path graph search on a positive directed or
    undirected graph.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    method : string ['auto'|'FW'|'D'], optional
        Algorithm to use for shortest paths.  Options are:

           'auto' -- (default) select the best among 'FW', 'D', 'BF', or 'J'
                     based on the input data.

           'FW'   -- Floyd-Warshall algorithm.
                     Computational cost is approximately ``O[N^3]``.
                     The input csgraph will be converted to a dense representation.

           'D'    -- Dijkstra's algorithm with Fibonacci heaps.
                     Computational cost is approximately ``O[N(N*k + N*log(N))]``,
                     where ``k`` is the average number of connected edges per node.
                     The input csgraph will be converted to a csr representation.

           'BF'   -- Bellman-Ford algorithm.
                     This algorithm can be used when weights are negative.
                     If a negative cycle is encountered, an error will be raised.
                     Computational cost is approximately ``O[N(N^2 k)]``, where 
                     ``k`` is the average number of connected edges per node. 
                     The input csgraph will be converted to a csr representation.

           'J'    -- Johnson's algorithm.
                     Like the Bellman-Ford algorithm, Johnson's algorithm is 
                     designed for use when the weights are negative. It combines 
                     the Bellman-Ford algorithm with Dijkstra's algorithm for 
                     faster computation.

    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.
    overwrite : bool, optional
        If True, overwrite csgraph with the result.  This applies only if
        method == 'FW' and csgraph is a dense, c-ordered array with
        dtype=float64.
    indices : array_like or int, optional
        If specified, only compute the paths from the points at the given
        indices. Incompatible with method == 'FW'.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.
    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    As currently implemented, Dijkstra's algorithm and Johnson's algorithm
    do not work for graphs with direction-dependent distances when
    directed == False.  i.e., if csgraph[i,j] and csgraph[j,i] are non-equal
    edges, method='D' may yield an incorrect result.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import shortest_path

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

    >>> dist_matrix, predecessors = shortest_path(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    
    floyd_warshall(csgraph, directed=True, return_predecessors=False,
                   unweighted=False, overwrite=False)

    Compute the shortest path lengths using the Floyd-Warshall algorithm

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.
    overwrite : bool, optional
        If True, overwrite csgraph with the result.  This applies only if
        csgraph is a dense, c-ordered array with dtype=float64.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import floyd_warshall

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3


    >>> dist_matrix, predecessors = floyd_warshall(csgraph=graph, directed=False, return_predecessors=True)
    >>> dist_matrix
    array([[0., 1., 2., 2.],
           [1., 0., 3., 1.],
           [2., 3., 0., 3.],
           [2., 1., 3., 0.]])
    >>> predecessors
    array([[-9999,     0,     0,     1],
           [    1, -9999,     0,     1],
           [    2,     0, -9999,     2],
           [    1,     3,     3, -9999]], dtype=int32)

    
    dijkstra(csgraph, directed=True, indices=None, return_predecessors=False,
             unweighted=False, limit=np.inf, min_only=False)

    Dijkstra algorithm using Fibonacci Heaps

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of non-negative distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j] and from
        point j to i along paths csgraph[j, i].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j or j to i along either
        csgraph[i, j] or csgraph[j, i].
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.
    limit : float, optional
        The maximum distance to calculate, must be >= 0. Using a smaller limit
        will decrease computation time by aborting calculations between pairs
        that are separated by a distance > limit. For such pairs, the distance
        will be equal to np.inf (i.e., not connected).

        .. versionadded:: 0.14.0
    min_only : bool, optional
        If False (default), for every node in the graph, find the shortest path
        from every node in indices.
        If True, for every node in the graph, find the shortest path from any
        of the nodes in indices (which can be substantially faster).

        .. versionadded:: 1.3.0

    Returns
    -------
    dist_matrix : ndarray, shape ([n_indices, ]n_nodes,)
        The matrix of distances between graph nodes. If min_only=False,
        dist_matrix has shape (n_indices, n_nodes) and dist_matrix[i, j]
        gives the shortest distance from point i to point j along the graph.
        If min_only=True, dist_matrix has shape (n_nodes,) and contains for
        a given node the shortest path to that node from any of the nodes
        in indices.
    predecessors : ndarray, shape ([n_indices, ]n_nodes,)
        If min_only=False, this has shape (n_indices, n_nodes),
        otherwise it has shape (n_nodes,).
        Returned only if return_predecessors == True.
        The matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    sources : ndarray, shape (n_nodes,)
        Returned only if min_only=True and return_predecessors=True.
        Contains the index of the source which had the shortest path
        to each target.  If no path exists within the limit,
        this will contain -9999.  The value at the indices passed
        will be equal to that index (i.e. the fastest way to reach
        node i, is to start on node i).

    Notes
    -----
    As currently implemented, Dijkstra's algorithm does not work for
    graphs with direction-dependent distances when directed == False.
    i.e., if csgraph[i,j] and csgraph[j,i] are not equal and
    both are nonzero, setting directed=False will not yield the correct
    result.

    Also, this routine does not work for graphs with negative
    distances.  Negative distances can lead to infinite cycles that must
    be handled by specialized algorithms such as Bellman-Ford's algorithm
    or Johnson's algorithm.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import dijkstra

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [0, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 3)	3

    >>> dist_matrix, predecessors = dijkstra(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    
    bellman_ford(csgraph, directed=True, indices=None, return_predecessors=False,
                 unweighted=False)

    Compute the shortest path lengths using the Bellman-Ford algorithm.

    The Bellman-Ford algorithm can robustly deal with graphs with negative
    weights.  If a negative cycle is detected, an error is raised.  For
    graphs without negative edge weights, Dijkstra's algorithm may be faster.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    This routine is specially designed for graphs with negative edge weights.
    If all edge weights are positive, then Dijkstra's algorithm is a better
    choice.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import bellman_ford

    >>> graph = [
    ... [0, 1 ,2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

    >>> dist_matrix, predecessors = bellman_ford(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

    
    johnson(csgraph, directed=True, indices=None, return_predecessors=False,
            unweighted=False)

    Compute the shortest path lengths using Johnson's algorithm.

    Johnson's algorithm combines the Bellman-Ford algorithm and Dijkstra's
    algorithm to quickly find shortest paths in a way that is robust to
    the presence of negative cycles.  If a negative cycle is detected,
    an error is raised.  For graphs without negative edge weights,
    dijkstra may be faster.

    .. versionadded:: 0.11.0

    Parameters
    ----------
    csgraph : array, matrix, or sparse matrix, 2 dimensions
        The N x N array of distances representing the input graph.
    directed : bool, optional
        If True (default), then find the shortest path on a directed graph:
        only move from point i to point j along paths csgraph[i, j].
        If False, then find the shortest path on an undirected graph: the
        algorithm can progress from point i to j along csgraph[i, j] or
        csgraph[j, i]
    indices : array_like or int, optional
        if specified, only compute the paths from the points at the given
        indices.
    return_predecessors : bool, optional
        If True, return the size (N, N) predecessor matrix.
    unweighted : bool, optional
        If True, then find unweighted distances.  That is, rather than finding
        the path between each point such that the sum of weights is minimized,
        find the path such that the number of edges is minimized.

    Returns
    -------
    dist_matrix : ndarray
        The N x N matrix of distances between graph nodes. dist_matrix[i,j]
        gives the shortest distance from point i to point j along the graph.

    predecessors : ndarray
        Returned only if return_predecessors == True.
        The N x N matrix of predecessors, which can be used to reconstruct
        the shortest paths.  Row i of the predecessor matrix contains
        information on the shortest paths from point i: each entry
        predecessors[i, j] gives the index of the previous node in the
        path from point i to point j.  If no path exists between point
        i and j, then predecessors[i, j] = -9999

    Raises
    ------
    NegativeCycleError:
        if there are negative cycles in the graph

    Notes
    -----
    This routine is specially designed for graphs with negative edge weights.
    If all edge weights are positive, then Dijkstra's algorithm is a better
    choice.

    If multiple valid solutions are possible, output may vary with SciPy and
    Python version.

    Examples
    --------
    >>> from scipy.sparse import csr_matrix
    >>> from scipy.sparse.csgraph import johnson

    >>> graph = [
    ... [0, 1, 2, 0],
    ... [0, 0, 0, 1],
    ... [2, 0, 0, 3],
    ... [0, 0, 0, 0]
    ... ]
    >>> graph = csr_matrix(graph)
    >>> print(graph)
      (0, 1)	1
      (0, 2)	2
      (1, 3)	1
      (2, 0)	2
      (2, 3)	3

    >>> dist_matrix, predecessors = johnson(csgraph=graph, directed=False, indices=0, return_predecessors=True)
    >>> dist_matrix
    array([0., 1., 2., 2.])
    >>> predecessors
    array([-9999,     0,     0,     1], dtype=int32)

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